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A group of methods for determining the complex refractive index spectra is based on the analysis of spectra of the attenuation coefficient and absorption coefficient of dispersions of particles.
A conceptually simple method has been developed for dispersions by Bricaud A and Morel 1986 and improved by Stramski D et al 1988. It begins with fitting, to the absorption spectrum of the particle material, a sum of Gaussian functions, each representing an oscillator that models a particular spectral peak of that spectrum. This yields a spectrum of the imaginary part, m"(λ), of the refractive index, where λ is the wavelength of light in vacuum. Once the parameters of the oscillators are known, a spectrum of the real part, m'(λ), can be calculated by using Ketteler-Helmholtz theory which relates the imaginary and real parts of the refractive index. This method is also known as dispersional analysis.
Note that the absorption spectrum of the particle material may differ from that of a dispersion of the particles due to the pigment packaging effect (see Absorption coefficient and Pigment packaging: Absorption spectra of dispersions). Hence, the absorption coefficient spectrum of the dispersion cannot be used directly for the determination of the imaginary part of the refractive index of the particle material. Obtaining the absorption spectrum of particles from the absorption spectrum of their dispersion is not a trivial task, given that it involves a model of interaction of light with the particles and thus requires (usually simplifying) assumptions regarding the size distribution, and other properties of the particle.
The task of determining the refractive index of particles which negligibly absorb light is somewhat simplified because a light scattering model alone can be used to determine the real refractive index, m = m', of the particles by fitting the data on the attenuation coefficient (here equal to the scattering coefficient) for a dispersion of the particles (for example, Katz A et al 2005, Carder KL et al 1972). Carder et al used ADA for marine phytoplankton (Isochrysis galbana, cell size ~4 µm, m = 1.023 to 1.032, relative to seawater), while Katz et al used GRA, a statistical interpretation of ADA to determine time-evolution of the size (0.38 µm to 0.6 µm) and refractive index (ranging from 1.51 to 1.39, relative to air) of activated spores of Baccilus subtilis from light scattering spectra of the spores' suspension. Katz et al also used a coated-sphere model of GRA to closely decribe the observed evolution of the spore structure after a heat shock.
The real part of the refractive index of particles can also be determined by immersion refractometry.
The complex refractive index of a substance can also be derived by Kramers-Krönig (KK) analysis of optical spectra, as it has been done for water (for example, Querry MR et al 1991). Bernard S et al 2001, who compared the results of determination of the complex refractive index of natural dispersions with the two KK methods and a dispersional analysis method, note the advantages of the KK method despite computational and difficulties. Such difficulties are summarized, for example, by Toon OB et al 1976. Kuzmenko AB 2005 developed a variational method of the KK analysis, a limiting case of the dispersional analysis. Here, the number of oscillators is on the order of magnitude of the number of data points in a spectrum. A significant advantage of Kuzmenko's method is its ability to use many different spectra (reflectance, transmittanse, ellipsometry, ATR, ...) of various types of samples (bulk material, suspensions, thin films, multilayers, ...). Kuzmenko's method is implemented in a computer program.
Ma X et al 2003 used another approach in the determination of the complex refractive index spectra of polystyrene spheres (see also Refractive index of polystyrene). They interpreted results of measurements of the absorption and attenuation of light by suspensions of micrometer-sized polystyrene spheres by using Monte Carlo simulations of radiative transfer in a dispersion of these particles.
| CITATION: Jonasz M. 2006. Refractive index from optical spectra (www.tpdsci.com/Tpc/RIbySpt.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 03-Apr-2006 Modified: 03-Jul-2009 Peer-reviewed: 13-Nov-2007 |
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